Crystallography Basics - Review

- They can fill an infinite plane and can be arranged in different ways on lattice Identical (same) environment: Same environment and basis positions after 2 different lattice translations in ‘blue’ :

2 Crystallography Basics (continued)

R Translation (lattice) vector

lattice parameters

For example, if we want to go from one corner to another across a body diagonal……. 3 Crystallography Basics (continued)

[uvw]:

[001] [011] [325]=?

[101] [111]

[100] [110]

3-D lattice showing position vector (R or r) = primitive (or If a,b,c cell lengths are lattice) vectors a, b and c with integer coefficients u, v and w different, e.g. orthorhombic If a,b,c cell lengths are equal, e.g. cubic

4 The Four 2-D Crystal Systems (Shapes)

2-D lattice showing position vector (R) = primitive (or lattice) vectors a and b with integer coefficients u and v:

The four 2-D crystal systems: (a) square, (b) rectangular, (c) hexagonal and (d) oblique:

These are the only 4 possible 2-D crystal systems

5 Crystallography Basics (continued)

180° in-plane (2-fold) Mirror planes rotation Mirror planes (reflection)

6 Crystallography Basics (continued)

* *Recently quasicrystals were discovered and do not belong to 1 of 230

7 The Seven 3-D Crystal Systems (Shapes)

Unit cell: smallest repetitive volume which contains the complete lattice pattern of a crystal.

from your Callister Book

These are the only 7 possible 3-D crystal systems 8 (know them and their 6 lattice parameters) The Seven 3-D Crystal Systems (continued) Monoclinic- has 2-fold rotation (180°) normal to the centers of 2 unit cell edges going through the opposite sides of the cell, e.g. {01ī} has 2-fold symmetry denoted with diad shape.

Trigonal - has 3-fold rotation (120°) normal to the body diagonal, e.g. {11ī} has 3-fold symmetry denoted with triangle shape.

Cubic- has 2,3 and 4-fold (90°) rotations, e.g. {001} has 4-fold symmetry denoted with square shape.

9 Cubic Crystal System Symmetry

From John D. Verhoeven, Fundamentals of Physical Metallurgy, Wiley, New York, 1975, p. 16

10 Summary of the Seven 3-D Crystal Systems